Adaptive spectroscopic visible-light optical coherence tomography for clinical retinal oximetry

Background Retinal oxygen saturation (sO2) provides essential information about the eye’s response to pathological changes that can result in vision loss. Visible-light optical coherence tomography (vis-OCT) is a noninvasive tool that has the potential to measure retinal sO2 in a clinical setting. However, its reliability is currently limited by unwanted signals referred to as spectral contaminants (SCs), and a comprehensive strategy to isolate true oxygen-dependent signals from SCs in vis-OCT is lacking. Methods We develop an adaptive spectroscopic vis-OCT (ADS-vis-OCT) technique that can adaptively remove SCs and accurately measure sO2 under the unique conditions of each vessel. We also validate the accuracy of ADS-vis-OCT using ex vivo blood phantoms and assess its repeatability in the retina of healthy volunteers. Results In ex vivo blood phantoms, ADS-vis-OCT agrees with a blood gas machine with only a 1% bias in samples with sO2 ranging from 0% to 100%. In the human retina, the root mean squared error between sO2 values in major arteries measured by ADS-vis-OCT and a pulse oximeter is 2.1% across 18 research participants. Additionally, the standard deviations of repeated ADS-vis-OCT measurements of sO2 values in smaller arteries and veins are 2.5% and 2.3%, respectively. Non-adaptive methods do not achieve comparable repeatabilities from healthy volunteers. Conclusions ADS-vis-OCT effectively removes SCs from human images, yielding accurate and repeatable sO2 measurements in retinal arteries and veins with varying diameters. This work could have important implications for the clinical use of vis-OCT to manage eye diseases.


Supplementary Notes 1. Ex vivo phantom validation and in vivo comparison
We measured sO2 values in an ex vivo bovine blood phantom using vis-OCT and compared them with a blood-gas analyzer (Rapidlab 248, Siemens Healthcare Diagnostics, Malvern, PA). We pulled a glass capillary tube to an inner diameter of ~ 200 m (Fig. S1a). We embedded the pulled tube in the middle of a homemade plastic well (Fig. S1b). To reduce specular reflections from the air-glass interface, we added immersion oil (refractive index = 1.52) to the well until the tube was covered by ~ 500 m of oil.
Next, we prepared oxygenated (sO2 ≈ 100%) and deoxygenated (sO2 ≈ 0%) bovine blood (Quadfive, Ryegate, MT). The hematocrit of blood samples was 45%. To oxygenate blood, we exposed it to a constant stream of pure oxygen while mixing with a magnetic stir bar. We verified that the blood was oxygenated using the blood-gas machine. To deoxygenate blood, we added sodium dithionite to the solution 1 . We monitored the partial pressure of oxygen (pO2), partial pressure of carbon dioxide (pCO2), pH, and temperature of the mixture using the blood-gas machine and converted to sO2 2 . We continued adding sodium dithionite and measuring sO2 until the blood was sufficiently deoxygenated. Following oxygenation and deoxygenation, we immediately loaded blood samples into syringes to prevent influences from ambient air.
We used oxygenated and deoxygenated samples to make 17 blood samples between sO2 ≈ 100% and sO2 ≈ 0%. To this end, we mixed oxygenated and deoxygenated samples to create blood of another oxygenation level. We measured sO2 of the mixed blood using the blood-gas machine. We imaged each blood sample immediately after the blood-gas machine measurement.
Before loading blood into the tube, we flushed the tube with a phosphate-buffered saline (PBS) and heparin solution to prevent clotting or sedimentation. Then, we loaded the blood into a syringe, which was connected to the glass tube by ~ 1 m of plastic tubing. We placed the syringe in a syringe pump (Model-Fusion 100, Chemyx, Inc. Stafford, TX), which flowed the blood at ~ 0.03 mm/s inside the glass tube to prevent clotting or sedimentation.
Before imaging, we focused the beam on the tube by adjusting the tube height and maximizing the intensity of backscattered light. After reaching the best focus, we adjusted the reference arm to place the top of the tube < 100 m from the zero delay. Then, we imaged the tube using a 512 x 512 raster scan. The optical power incident on the tube was 1.20 mW. After imaging each blood sample, we re-flushed the tube with PBS and heparin solution.
We measured sO2 with vis-OCT in each blood sample using the Ads-OCT processing proposed in this work. Since scattering factor was not well-agreed upon in the literature, we varied SSF to find the highest spectral fit R 2 . We found that the best spectral fit R 2 was reached between 0.02 ≤ ≤ 0.10.
We computed 100 vis-OCT sO2 measurements for each tube. Briefly, we processed and stored all 512 B-scans. Then, we randomly selected and averaged 50 different B-scans from this set for sO2 measurement. Then, we refreshed the 512 B-scans and repeated random selection 100 times to reach 100 sO2 measurements.
Fig. S2a shows tube sO2 measured by vis-OCT and the blood-gas machine for 17 tubes ranging from sO2 ≈ 0% to sO2 ≈ 100%. The equation of the best-fit line is = (1.01 ± 0.024) + 1.28 and the coefficient of regression is 2 = 0.97. Using the standard error of the slope of the regression fit, we estimate the sensitivity of our measurement in phantoms to be 2.4%. The relationship between the blood-gas machine and vis-OCT sO2 was nearly a slope of 1 with only ~1% bias. This was within our target accuracy, so we did not apply a post-hoc calibration curve to vis-OCT measurements in this work. considering the increased spatial averaging for larger vessels. Nevertheless, R 2 did not have a significant influence on the sO2 value.

Supplementary Notes 2. Statistical advantage of depth averaging
The depth-resolved slope of NL-SDA-lines (further referred to as the "slope method") was previously used to extract the attenuation coefficient of OCT signals in Step 8 in Fig. 2 [3][4][5] . In this work, we found that the depth-resolved average of NL-SDA-lines (further referred to as the "depthaveraging method") was statistically advantageous to the slope method for retinal oximetry. We compared the two methods for sO2 measurements in the 125 unique human retinal vessels described above. Both sO2 measurements used identical AdS-vis-OCT processing with identical depth-selection windows. To implement the slope method, only the depth-averaging step, as depicted by Step 8 in the AS-OCT processing, was replaced with a simple linear regression to estimate the slopes of NL-SDA-lines along the -axis. The comparisons between the two methods demonstrate that the depth-averaging method greatly improves the stability of vis-OCT retinal oximetry than the slope method.
Empirically, we found that depth-averaging the natural logarithm of the SDA-lines yielded less noisy spectra, as compared with the slope method (Table S2). We verified these empirical observations by Monte Carlo simulation. To begin, we applied the slope method and depthaveraging method to the equation of a line, which is predicted by Eqn. 7 in Methods. (for simplification, removing small effect of LCA): where 1 is an arbitrary constant and is random, normally distributed noise. was a 30-pixel vector ranging from 0 to 35 for the depth selection window. We used the slope method to compute the slope of Eq. S1 and directly find 1 . We used the depth-averaging method to compute the average value of Eq. S1 (similar to Eq. 8) to find the constant 1 ∝ 1 . We computed 10 5 iterations of such measurements and then measured their coefficients of variation: where value of 1 1 was independent of 1 and . This suggested that the depth-averaging method had an intrinsic noise reduction advantage of 67% over the slope method for additive, normally distributed noise.
In reality, however, the SDA-lines follow an exponential decay with the additive noise. We applied a natural logarithm to this function: One frequent assumption by the slope method is that signal is significantly greater than the noise, or − 1 ≫ , after which Eq. S3 would converge to a noiseless version of Eq. S1. However, in the human retina, SNR is often low, and this assumption might not be correct. To this end, the noise in Eq. S3 after the natural logarithm is less trivial than in Eq. S1 since there is no longer a linear relationship between 1 and . We repeated the simulation described above, except we generated the signal and noise using Eq. S3. for this simulation. Like the analysis from Eq. S1, the coefficient of variation using the slope method is always higher than that using the depth averaging method. However, the 1 1 is not constant and increases with increased 1 . This is because the relationship between 1 and is nonlinear in Eq. S3. This has important implications for the slope method in sO2 calculation since the measured blood spectrum can have different noise levels for different wavelengths and different depth selection windows. In this work, we demonstrated empirically that depth averaging is statistically advantageous over the slope method for sO2 calculation, consistent with the simulation.

Supplementary Notes 3. Influence of Polarization in vis-OCT Retinal Oximetry
Since the anisotropic form factor and arbitrary orientation of the RBCs change the polarization state of the scattered light unpredictably, the influence of polarization on the measured spectrum needs to be considered. Thus, we mitigated the polarization dependence of the scattered light on the measured spectrum. First, we used a 300 MHz pulse repetition supercontinuum laser, which emits a randomly polarized broadband light changing from pulse to pulse. During the A-scan exposure time of 38 µs of the line-scan camera in our spectrometer, we averaged out multiple random polarization states illuminating RBCs. Second, most photons detected from the blood vessel are multiply scattered photons 6 . As each scattering event alters polarization, returning photons scattered by blood have a broad range of polarizations. As we averaged A-lines at multiple positions across several B-scans, our measured spectrums for blood capture the influence of a wide range of polarizations. Finally, the depth-resolved nature of ADS-vis-OCT and normalization of the signal at the blood maximum eliminates any differences in polarization-dependent backscattering between blood and tissue, which typically influence the relative contribution of outof-blood tissue scattering and blood absorption in non-depth resolved measurements 7 .

Supplementary Notes 4. Longitudinal Chromatic Aberration in vis-OCT Retinal Oximetry
We developed an approach for fitting LCA transfer functions to sO2 measurement using the physical optics of the human eye. First, we simulated the CFS in the human eye model from Polans et al. 8 using Optic Studio 16 (Zemax, Kirkland, Washington). Since the wavelength ranges and lateral resolutions of the vis-OCT systems used in this study were approximately the same (see Methods -Vis-OCT Systems), we used the same CFS for both systems (Fig. S4a). The simulated chromatic focal shift (CFS) CFS is consistent with that previously measured in the human eye 9 .
Then, we calculated potential LCA transfer functions using a modified version of the equation used in 10 to account for spectroscopic analysis: where 550 is the reference focusing depth at 550 nm, for each of the 41 focal positions (Fig. S4c).
To understand the potential influence of LCA on sO2 measurement, we simulated SDAlines in a vessel consistent with the Beer-Lambert law and the attenuation spectra in Faber et al. 11 . We multiplied � ( , ) at each focal position with the SDA-lines to account for LCA (Eqn. 1) and took its natural logarithm. We averaged the spectrum at the same depths used to find ( , ) (Eqn. 8 in Methods). We noted that for all simulated physiological sO2 measurements (sO2 = 40% to sO2 = 100%) and focal positions, the peak-to-peak amplitude of ( , ) was less than 0.25 times the peak-to-peak amplitude of ( ) �( 0 − ) + Δ 2 �. We used this relationship to constrain physically reasonable ( , ) to avoid overfitting this parameter in the sO2 measurement. Furthermore, since the above constraint described relative amplitudes only, it was an independent optical power incident on the vessel.
We measured sO2 in the above simulation without and with LCA fitting described in

Stage 2:
First, we rejected all sO2 iterations where the spectral fit 2 < 0.80. We found that noisier arterial spectra resulted in sO2 = 100%, which saturates at the maximum possible value.
Therefore, we also rejected iterations where sO2 = 100% and 2 < 0.93. Next, we sorted the iterations in ascending order of sO2 and selected the 20 central indexes, acting as a pseudo-median measurement. Among these values, we selected the iteration where the 2 was the highest. We saved the , , and for the selected iteration and accepted the sO2 with these parameters.

Parameter iterations:
We introduced small variations in three parameters we identified as sensitive to sO2. The first parameter is , the identified depth where the blood signal begins to decay. After STFT, the axial resolution of ~ 9 and spatial averaging between B-scans broadens the peak blood backscattering signal, adding uncertainty to its localization. Furthermore, random or unknown parameters, such as speckle noise, erythrocyte spatial distributions, and vis-OCT illumination beam's incidence angle, may contribute to depth-dependent spectroscopic signal differences in vessels. Therefore, we tuned from 6 to 14 in 8 equidistant steps below the identified peak blood signal and computed sO2 for each iteration. If a single peak could not be found, perhaps due to noise or spatial averaging, we then tuned from 16 to 24 in 8 equidistant steps from the peak amplitude of the anterior vessel wall. The second parameter is the scattering scaling factor SSF, which can vary with erythrocyte spatial distributions and multiple scatterings 6 . Based on ex-vivo bovine blood sO2 measurements and human retinal sO2 measurements, we determined that the strongest regression fits ( 2 ) were found between SSF = 0.02 and SSF = 0.10. This is consistent with our previous findings 6 . Therefore, we computed eight iterations of sO2 for SSF in this range with a step size of 0.01. The third parameter scales the SDBG amplitude by a small value. Briefly, we measured the SDBG where the vis-OCT signal was attenuated to the noise floor and extrapolated its amplitude at the vessel location by fitting an exponential curve to the SDBG. Due to the low SNR of the measured spectrum relative to the SDBG, small errors in this extrapolation could alter the measured spectrum. To account for these potential errors, we applied a small correction factor to the SDBG, ( , ), before SDBG subtraction from Eq. 1. We tuned between 0.96 and 1.04 in 9 steps with a step size of 0.01. We measured sO2 for each iteration (Fig. 2, Step 8). In total, we calculated sO2 for 8 × 8 × 9 = 576 iterations. We stored measured sO2 and spectral fit R 2 for each parameter iteration in 3D matrixes.

Fixed-attenuation measurement parameters:
We computed sO2 measurements for a non-adaptive method referred to as 'fixed attenuation' (FA Method; see Results -Comparison with non-adaptive retinal oximetry). Rather than compute optimal depths for normalization and spectroscopic measurement, we used rigid parameters. For , normalization depth, we selected 23 µm below the peak signal from the anterior vessel wall; for 0 , starting depth of spectroscopic measurement, we selected 8 µm after ; for ∆ , spectroscopic measurement range, we selected 36 µm below 0 . If the rigid parameters did not fit inside of a smaller vessel (diam < 60 µm), we manually reduced the depth range to fit inside the vessel. These parameters were all within the ranges specified in Ads-vis-OCT.   Coefficient of variation ratio between slope and depth averaging methods for estimating attenuation coefficient. Exponential decay model from Eq. S3 is used for calculations. 1 is attenuation coefficient estimated by slope method; 1 is proportional to 1 and estimated by the depth averaging method.